Prime factorization of $$$1925$$$
Your Input
Find the prime factorization of $$$1925$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1925$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1925$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1925$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$1925$$$ by $$${\color{green}5}$$$: $$$\frac{1925}{5} = {\color{red}385}$$$.
Determine whether $$$385$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$385$$$ by $$${\color{green}5}$$$: $$$\frac{385}{5} = {\color{red}77}$$$.
Determine whether $$$77$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$77$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$77$$$ by $$${\color{green}7}$$$: $$$\frac{77}{7} = {\color{red}11}$$$.
The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.
Since we have obtained $$$1$$$, we are done.
Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $$$1925 = 5^{2} \cdot 7 \cdot 11$$$.
Answer
The prime factorization is $$$1925 = 5^{2} \cdot 7 \cdot 11$$$A.